A bus covered a certain distance from village A to village B at the speed of 60 km/hr. However, on its return journey it got stuck in traffic and covered the same distance at the speed of 40 km/hr and took 2 hours more to reach its destination. What is the distance covered between villages A and B?

### Concept & Formula When the same distance is covered at two different speeds, the difference in travel times can be used to find the distance. $$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$ ### Step-by-Step Solution Let the distance between villages A and B be $D$ km. - Time taken from A to B at $60$ km/hr: $$t_1 = \frac{D}{60}$$ - Time taken on the return journey at $40$ km/hr: $$t_2 = \frac{D}{40}$$ The return journey took $2$ hours more: $$\frac{D}{40} - \frac{D}{60} = 2$$ Taking $120$ as the common denominator: $$\frac{3D-2D}{120}=2$$ $$\frac{D}{120}=2$$ Therefore, $$D=240\text{ km}$$ ### Exam Strategy & Shortcut For the same distance covered at speeds $v_1$ and $v_2$, with a time difference of $t$: $$D = \frac{t v_1 v_2}{v_1-v_2}$$ Here, $$D=\frac{2\times60\times40}{60-40}=240\text{ km}$$ This shortcut quickly gives the distance without separately calculating both times. ### Common Pitfall A common mistake is to use the average speed of $50$ km/hr. The two journeys do not take equal amounts of time, so averaging the speeds does not solve the problem. Instead, use the given **2-hour difference in travel time**. ### Final Answer Therefore, the correct answer is **240 km**.